Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

Blackbody emission under laser excitation of silicon nanopowder produced by plasma-enhanced chemical-vapor deposition

Previous results concerning radiative emission under laser irradiation of silicon nanopowder are reinterpreted in terms of thermal emission. A model is developed that considers the particles in the powder as independent, so under vacuum the only dissipation mechanism is thermal radiation. The supralinear dependence observed between the intensity of the emitted radiation and laser power is predicted by the model, as is the exponential quenching when the gas pressure around the sample increases. The analysis allows us to determine the sample temperature. The local heating of the sample has been assessed independently by the position of the transverse optical Raman mode. Finally, it is suggested that the photoluminescence observed in porous silicon and similar materials could, in some cases, be blackbody radiation

Gas collisions and pressure quenching of the photoluminescence of silicon nanopowder grown by plasma-enhanced chemical vapor deposition

The quenching of the photoluminescence of Si nanopowder grown by plasma-enhanced chemical vapor deposition due to pressure was measured for various gases ( H2, O2, N2, He, Ne, Ar, and Kr) and at different temperatures. The characteristic pressure, P0, of the general dependence I(P)=I0exp(-P/P0) is gas and temperature dependent. However, when the number of gas collisions is taken as the variable instead of pressure, then the quenching is the same within a gas family (mono- or diatomic) and it is temperature independent. So it is concluded that the effect depends on the number of gas collisions irrespective of the nature of the gas or its temperature

Determination of the direct band-gap energy of InAlAs matched to InP by photoluminescence excitation spectroscopy

A series of InxAl1-xAs samples (0.51≪x≪0.55)coherently grown on InP was studied in order to measure the band-gap energy of the lattice matched composition. As the substrate is opaque to the relevant photon energies, a method is developed to calculate the optical absorption coefficient from the photoluminescence excitation spectra. The effect of strain on the band-gap energy has been taken into account. For x=0.532, at 14 K we have obtained Eg0=1549±6 meV

Oxidation of silicon: further tests for the interfacial silicon emission model

The classical description of Si oxidation given by Deal and Grove has well-known limitations for thin oxides (below 200 Ã). Among the large number of alternative models published so far, the interfacial emission model has shown the greatest ability to fit the experimental oxidation curves. It relies on the assumption that during oxidation Si interstitials are emitted to the oxide to release strain and that the accumulation of these interstitials near the interface reduces the reaction rate there. The resulting set of differential equations makes it possible to model diverse oxidation experiments. In this paper, we have compared its predictions with two sets of experiments: (1) the pressure dependence for subatmospheric oxygen pressure and (2) the enhancement of the oxidation rate after annealing in inert atmosphere. The result is not satisfactory and raises serious doubts about the model’s correctness

Quantification of the bond-angle dispersion by Raman spectroscopy and the strain energy of amorphous silicon

A thorough critical analysis of the theoretical relationships between the bond-angle dispersion in a-Si, Δθ, and the width of the transverse optical Raman peak, Γ, is presented. It is shown that the discrepancies between them are drastically reduced when unified definitions for Δθ and Γ are used. This reduced dispersion in the predicted values of Δθ together with the broad agreement with the scarce direct determinations of Δθ is then used to analyze the strain energy in partially relaxed pure a-Si. It is concluded that defect annihilation does not contribute appreciably to the reduction of the a-Si energy during structural relaxation. In contrast, it can account for half of the crystallization energy, which can be as low as 7 kJ/mol in defect-free a-Si

Microstructure and magnetic properties of Ni50 Mn37 Sn13 Heusler alloy ribbons

The Heusler alloy Ni50 Mn37 Sn13 was successfully produced as ribbon flakes of thickness around 7-10 μm melt spinning. Fracture cross section micrographs in the ribbon show the formation of a microcrystalline columnarlike microstructure, with their longer axes perpendicular to the ribbon plane. Phase transition temperatures of the martensite-austenite transformation were found to be MS =218 K, Mf =207 K, AS =224 K, and Af =232 K; the thermal hysteresis of the transformation is 15 K. Ferromagnetic L 21 bcc austenite phase shows a Curie point of 313 K, with cell parameter a=0.5971 (5) nm at 298 K, transforming into a modulated 7M orthorhombic martensite with a=0.6121 (7) nm, b=0.6058 (8) nm, and c=0.5660 (2) nm, at 150 K